I keep my phone in a Faraday bag. Nothing gets in or out until I decide. Messaging and emails will keep trying to get thru, buffering at your ISP until your phone pings a tower. Once you remove it from the Velcro enclosed bag it takes about a minute to ping a tower and receive data. Do what you need with your phone and then put it back in the bag. Just like that, poof! It disappears.
Brand/model recommendations if you could?
Do you have a favorite brand?